Formation of asset allocation inputs (Week 4)

Question 1

Modern Portfolio theory assume

Answer 1

All investors have same expectation of asset returns.

Assumed the asset returns are Identically and independently distributed. All market portfolio they have the same probability distribution. (return generation process is stable for one asset do not accommodate changes for risky assets)

Question 2

Forming asset assumptions

Answer 2

1. Asset Assumptions: return, variance, covariance
2. Start from objectives (ALWAYS!): link client objectives to the data assumptions, e.g. data interval, sample period, etc.
3. Lots of choices to make

Question 3

What does “forming asset assumptions” mean in asset allocation?

Answer 3

A

Forecast asset expected returns.

B

Forecast covariance of all aset classes in the portfolio.

D

Forecast standard deviation for all assets in the portfolio.

Question 4

Quantitative analysis using historical returns is non-trivial part of the asset allocation process.

Select all of the correct statements about data selection in portfolio analysis

Answer 4

B Data selection has to be linked to investor’s objectives and investment horizon.

C

It’s more likely to capture the entire distribution with longer data period, but it’s also more likely to include structural changes, i.e. some data in the past maybe not relevant for the forecast period.

F

It’s ultimately a trade-off. Longer data intervals may mitigate the data problem as a result of thin trading or appraisal based valuations, but you end up with less data points in short period of time.

Question 5

Slide 3

To forecast the expected returns of a group of assets, which methods below are appropriate?

Answer 5

Implied views method that let the model generate expected returns conditional on the variance-covariance metrics so that a user-specified portfolio (e.g. the benchmark) is the optimal portfolio on the efficient frontier.

C

Bayesian technique, for instance, James Stein estimator.

D

Black-Litterman approach that combines market equibrium and investor’s expectations.

Question 6

Confidence interval around per-annum expected return

Answer 6

usually narrows with investment horizon.

as “variance” or “risk” in a general sense is spread over more periods with longer investment horizon when it’s measured on per-period or per-annum returns. Over long term, returns tend to converge to mean. Variance tends to reduce with investment horizon.

Question 7

Confidence interval around wealth can

Answer 7

either widen or narrow with investment horizon.

wealth is an accumulation of all of the returns in each period over the entire investment horizon. Depending on how these period returns are correlated, confidence interval around wealth may widen or narrow with investment horizon

Question 8

Assume a return series demonstrates significant positive serial correlation. Which of the following statements is likely to be correct under this situation?

Answer 8

B

Variance of per annum returns tends to decrease with investment horizon.

C

Variance of wealth tends to increase with investment horizon.

D

Variance of per annum returns tends to increase with investment horizon.

E

The underlying asset may be thinly-traded.

Question 9

Variance of wealth tends to

Answer 9

When a return series demonstrates significant positive serial correlation, it’s most likely variance of wealth tends to increase with investment horizon because the “momentum” builds up over multiple periods over the investment horizon. The longer the investment horizon, the more “momentum” is incorporated in wealth which is (1+Rt1)(1+Rt2)…. Variance of per annum or per-period returns may increase or decrease over longer investment horizon even though significant positive serial correlation presents as they are measured in per period term

Question 10

Data selection in portfolio analysis

Answer 10

• has to be linked to investor’s objectives and investment horizon. align data period with investment horizon. in practice, have longer investment horizon than data period

Question 11

benefit and disadvantage of longer data period

Answer 11

• capture the entire distribution
• include structural changes e.g. some data in the past may not be relevant for the forecast period

Question 12

Choosing daily and weekly data

Answer 12

is problematic due to high serial correlation. most quantitative measure of risk assumes the returns are independent.

monthly or quarterly should be preferred

Question 13

When do you exclude an outlier

Answer 13

no chance of this negative market event happening at all.

may reduce the impact of these but do not delete the outliers from time series

Question 14

Longer data interval trade off

Answer 14

mitigate the data problem as a result of thin trading and appraisal based valuations

but you end up with less data points in a short period of time

Question 15

when do you use historical mean of each asset class to forecast expected returns of a group of assets

Answer 15

never, unless you have 100 years of data

but even if you do, you would be including a lot of unrelated info

Question 16

mean variance optimisation has been described as

Answer 16

an unreliable method and optmisers have been error maximisers

Question 17

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

DP

Answer 17

Direct property is being influenced by appraisal valuations. This reduces measures of volatility at shorter horizons. The 3-year and 5-year standard deviations of about 11% are probably more representative of ‘true’ underlying volatility. Also note the large serial correlation for DP at quarterly intervals (0.80). This probably reflects a rolling quarterly revaluation cycle

Question 18

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

DP

Answer 18

Direct property is being influenced by appraisal valuations. This reduces measures of volatility at shorter horizons. The 3-year and 5-year standard deviations of about 11% are probably more representative of ‘true’ underlying volatility. Also note the large serial correlation for DP at quarterly intervals (0.80). This probably reflects a rolling quarterly revaluation cycle

Question 19

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

3

Answer 19

AE has a complex serial correlation pattern, which is slightly positive at monthly and quarterly intervals, but negative at yearly intervals. Its standard deviation is stable up to 1-year, before decreasing.

Question 20

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

2

Answer 20

Standard deviation of AC approaches then exceeds AFI and WFI as investment horizon increases. This reflects combination of high positive serial correlation (when cash rates start moving, they tend to keep going), plus fact that cash investments are ‘rolled over’ and hence ‘re-priced’

Question 21

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Standard deviations –Closer inspection reveals a relation with serial correlation

for example

Answer 21

For series with higher serial correlation, standard deviation tends to increase with investment horizon. Examples include WE, DP, AFI. WFI and (especially) AC.

Question 22

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

correlation

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 4

Answer 22

Correlations also tend to be lower over shorter horizons as short-term data is ‘noisier’, and hence can hide any underlying correlation structure. The latter begins to show through the noise as the measurement interval is lengthened.

Question 23

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

correlation

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 3

Answer 23

Over the longer term, all assets reflect the impact of common influences such as:

(a) broader economic and market trends, and
(b) realization of (positive) expected returns over the passage of time. This influences show up as a rise in correlation with holding period.

Question 24

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

correlation

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 2

Answer 24

DP returns reflect irregular appraisal valuations, which react gradually to market developments. This creates the appearance of no correlation with AE and LP at shorter horizons, as they react immediately to market developments.

Question 25

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

correlation

The correlations between AE and LP are relatively high and stable across holding periods. However, the correlation of AE and LP with DP is very low at monthly and quarterly horizons, but increases with time. Reasons for this pattern include:

Reason 1

Answer 25

AE and LP are both listed, and hence commonly reflect broader equity market fluctuations.

Question 26

The estimates for both standard deviation and correlation change across the various asset classes as measurement interval lengthens, so that ‘risk’ appears to vary with holding period. What might explain the movements you observe?

Answer 26

Std

correlation

Question 27

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

3.

Answer 27

Prevalence of serial correlation and/or measurement lags

n the data should be considered, e.g. thin-trading, appraisals. Lengthening the measurement interval will dilute the impact. The relevance of this issue can relate to the type of assets being analyzed (e.g. liquidity, valuation method)

Question 28

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

2.

Answer 28

Finer data means more data points. This is useful if there is a requirement to restrict the time period from which the data is drawn in order to generate ‘fresh’ estimates of risk measures such as standard deviation and covariance.

An example would be if there has been a structural change so that older data becomes less relevant. Estimates can be drawn from the recent part of the available history by cutting the data into finer intervals (e.g. monthly instead of annually)

Question 29

Considerations in selecting measurement interval

Ultimately it is a trade-off, including the following three considerations:

1.

Answer 29

Ideally align measurement interval with investment time horizon (or ‘review’ period) if practical.

Question 30

Considerations in selecting measurement period

Answer 30

1. Availability of data – this constrains what choice of period you have
2. Which period is most representative looking forward – Is the period long enough to capture all relevant events? Or could older data be misleading to instabilities such as structural change, etc?
3. Whether any instability can be successfully modeled – If so, a longer period may still be preferable to estimate the model

Question 31

Causes of instability in the series plotted

Std dev of WE

Answer 31

fluctuations in series for hedged WE largely reflects positioning of ‘crashes’ such as 1987, tech wreck and GFC

− difference between hedged and unhedged series reflects impact of currency, and the (changing) role of A$ as a ‘risk’ asset that is highly correlated with global equities – at least until recently

Question 32

Causes of instability in the series plotted

Std dev of AE:

Answer 32

• reduced sharply as 1987 crash dropped out measurement period (during 1997);

− positive structural change in the nature of Australian economy and markets over time probably generated a trend to more stable returns

− increase by 2017 reflects impact of GFC (Global Financial Crisis)

− reduced recently as the impact of GFC dropped out of the measurement period (10 years)

Question 33

Causes of instability in the series plotted

Correl WE vs Comm:

Answer 33

− commodities have a reputation for having a low correlation with equities. While this is often the case, the data reveals that this correlation varies through time. In recent years, the correlation has pushed well above 0.3.

− whether economic or inflation risk dominates can matter to this correlation, e.g. it moved higher during and after the GFC, as fluctuating concerns over economy dominated both equities and commodities

− the much-debated ‘financialization of commodities’ argument suggest that commodities may become more correlated with other assets due to the impact of investment flows

Question 34

Causes of instability in the series plotted

Correl of equities vs fixed income

Answer 34

correlation between equities and FI has been instable through time: it tends to reduce when inflation is low and uncertainty over the economy prevails, and increases when inflation is high.

− correlation became negative after mid-1990s, when the idea that inflation had been ‘defeated’ became widely accepted. This is seen in both series, with correlation of AE with AFI having been particularly negative over last decade or so

Question 35

Causes of instability in the series plotted

Std dev of WFI:

Answer 35

declined as interest rate volatility decreased with lower and more stable inflation over time

− diversification increased within the FI index itself due to broadening the range of securities beyond traditional government bonds, e.g. increasing credit component

Question 36

Causes of instability in the series plotted

Std dev of LP (Note: LP = REITs = Real Estate Investment Trusts)

Answer 36

− underlying change in nature of asset class occurred during the 2000’s, including pursuit of income sources other than traditional rentals (e.g. development profits) and higher leverage levels

− Sector was particularly hard hit during GFC for these reasons

− REITs have de-risked in recent years, and have been more stab

Question 37

Bayes-Stein estimators

how does it work

Answer 37

Observed sample means for individual assets are “shrunk” to some global mean

many cases, the greater the variability in the historical data, the greater the shrinkage of sample means to the global mean.

shrinking the recommended optimal mix in the direction of the minimum-variance efficient portfolio

Question 38

Bayes-Stein estimators

Answer 38

constitute an important class of admissible estimators of expected returns when historical data are used

Question 39

with monthly daily weekly data

Answer 39

Equity returns very high correlation

Question 40

Lots of choices to make:

Parametric/model-based

Answer 40

follow a certain distribution. Normally a normal distribution.

assume returns are identically and independently distributed. Calculate std and use to calculate return distribution.

Question 41

Non-parametric/Data based quantitative measures

Answer 41

e.g. probability of loss, average loss

Question 42

Problem with STD with Australian cash returns

Answer 42

Not independently distributed

Question 43

•What data to draw on:

–Measurement interval (unit of time)

–Time period

–Real or nominal?

Working with nominal is sufficient in

Answer 43

low inflation countries such as Australia

Real returns and non-inflation in emerging countries

Question 44

Lots of choices to make

Imputation credit

Answer 44

Giving tax credit is through imputation credits.

Australian companies have imputation level of 80%.

Question 45

Lots of choices to make

What about costs, taxes, alpha, etc

Answer 45

CGT and personal tax.

Question 46

Imputation credits and Australian investors

Answer 46

Australian investors expect 2% imputation credit. For Australia, total is 10%.

Investing in Australian firm is more attractive than other countries. That’s why they still have total portfolio invested in Australian assets

Question 47

Conditional assumptions

Why would you expect conditional forecasts to outperform an unconditional assumption?

Answer 47

Because conditional forecasts incorporate current available information.

Unconditional assumption (eg. Historical average) does not, or current information has very little weight in the assumption.

Question 48

is static conditional or unconditional

Answer 48

unconditional.

Do not incorporate any changes in investment opportunities or investor’s circumstances into my quantitative analysis

Question 49

Dynamic and tacitic, they are conditional or unconditional

Answer 49

they are conditional approach. Assume that investor’s circumstanes and opportunities will change in certain ways.

Conditional modelling incorporates latest available info, your judgment of what it’s going to involve.

Question 50

What happened in 1980s?

Answer 50

double digit inflation. High nominal and real IR

Question 51

Interest expectations will feed into

Answer 51

discount rate and asset returns. Cash rate, gov yield

One key parameter in forecast mode

Question 52

mean reversion is an important conditional assumption made in modelling

Mispricing

Answer 52

Do assets occasionally become mispriced?

Attempt to trade before correction

Question 53

mean reversion is an important conditional assumption made in modelling

What is the pace of reversion?

Answer 53

(link to investor’s horizon)

Interaction with liquidity concerns: can you afford to wait it out?

Question 54

mean reversion is an important conditional assumption made in modelling

Demonstrate how Risk premium follows a mean-reverting process during GFC

Answer 54

risk premium has raised to an unsustainable high level due to liquidity pressure, uncertainty of how the turmoil will end or just because investors were scared.

Afterwards, the risk premium of equity market did experience some kind of mean reverting process.

Question 55

Example of conditional modelling

Answer 55

Apply conditional assumption by forecasting mere reversion back to its PPP price which is 0.67c USD over 3 years given that there is a 3 year investment horizon. Long term expectation of a dollar

Condition modelling means I define the pace of mere reversion and how quickly 1 dollar will go back to market equilibrium price

Question 56

what data?

• measurement interval

Answer 56

1. Ideally we can have investment horizon aligned with data interval so we do not have to deal with multiple period in valuation period.
2. Influence of serial correlation / appraisals / thin trading fades as measurement interval is lengthened
3. –Longer intervals = less data points . Long historical returns not a problem.

• New assets e.g. listed infrastrcutures.
• Came into investors view in 1990s during global drive of privtisation and deregulation.

Question 57

•Time period

Answer 57

–Longer = more opportunity to see the entire distribution

–Longer = more exposure to any structure change

Question 58

When choosing sample period where you are going to choose historical returns

Answer 58

1987 stock market crash.

1993 the start of the current inflation and monetary policy and gradually inflation was tamed.

1999 onwards we had resource boom. Low standard deviation

Should you go back to 80s where we had double digit inflation or during 1999s when we had resource boom. Depend on our judgment and what we think will be more likely/ double digit not likely. Another resource boom depends

Question 59

Equity risk premium

Answer 59

we form our own estimation of Rf rate and equity risk premium and they are dynamic. Investment bank still issue their own forecast of equity risk premium 5%. Consensus is 3.5%

All of this is conditional modelling. Incororating Equity risk premium and risk free rate in your forecasting of aset returns. Incorporate the latest info. How financial market is going to evolve.

Question 60

Methods for calibrating expected returns

Answer 60

1.Use sample means

For a single asset class: historical means; impose expected returns

Easiest way is generating historical returns. Readily available. Free

Question 61

When can you use historical mean?

Answer 61

Want to use historical mean to represent the true population mean and return, neeed at least 100 years of data.

Even if you do, you will have to deal with structural changes. Never use historical means to characterize means to characterize future returns.

But if you run a historical estimation of std, it can be more usetul than the historical mean

Question 62

Problem with historical mean

Answer 62

Use 10, 20, 30. not likely going to have reasonable confidence interval that mean return will be close to true mean return.

Question 63

problem with daily returns and monthly data

Answer 63

Cannot make reasonable inferences from highly correlated data.

Question 64

data interval for Medium to long term investment horizon

Answer 64

prefer quarterly or yearly

Question 65

reasonable sample period

Answer 65

10y

Question 66

Methods for calibrating expected returns

Impose expected returns. Could be based on:

a)Linking to economy

b)Asset pricing model, e.g. cross-sectional risk (i.e. factor) model

Economic drivers

c) Investor’s forecasts

Answer 66

general equity market return, use real GDP growth of the country as a proxy

expected stock market level of Australian index. Can decompose that price into GDP, multiplied with the Aggregate level can estimate earnings of

PE multiple = how much you pay for one single unit from listed companies

Question 67

Methods for calibrating expected returns

Impose expected returns. Could be based on:

a) Linking to economy
b) Asset pricing model, e.g. cross-sectional risk (i.e. factor) model

Economic drivers

c) Investor’s forecasts

Answer 67

. I have this judgment insight. Just decide the e® of Australian equity is 8%. When you try to impose own expectation, trying to consider monetary policy, relative strength of AU economy relative to other economies. Consider what happened in the past and what we know right now.

Question 68

Methods for calibrating expected returns

Impose expected returns. Could be based on:

a) Linking to economy
b) Asset pricing model, e.g. cross-sectional risk (i.e. factor) model

Economic drivers

c) Investor’s forecasts

Answer 68

Real economic growth and inflation drive

Question 69

Methods for calibrating expected returns

Impose expected returns. Could be based on:

a) Linking to economy
b) Asset pricing model, e.g. cross-sectional risk (i.e. factor) model
c) Investor’s forecasts

Answer 69

generate factor loading of macroeconomic variables, fundamental characteristics of a firms (size, MTB ratio, industry etc.) that are driving the variation of returns across asset classes

Question 70

Methods for calibrating expected returns

impose ER

Answer 70

2. Impose expected returns. Could be based on:
   a) Linking to economy
   b) Asset pricing model, e.g. cross-sectional risk (i.e. factor) model
   c) Investor’s forecasts

Question 71

Methods for calibrating expected returns

3.Implied views

Answer 71

Have a benchmark portfolio.

Managing a balanced portfolio, im giving average performance of all of the balanced portfolios as benchmark to decide ranking, my performance.

Consider the consensus othey are holding an optimal portfolio. Don’t assume I am superior. Asssume the outcome of All of the balanced portfolio managers on aggregate level. Look at average asset allocation of these managers. Assume this portfolio is located on efficient frontier.

From there, Try to let mean variance model decide do own calculation to give set of expected returns all of th eassets within the portfolio. The average asset allocation of all managers is going to be the most efficient portfolio.

Question 72

Methods for calibrating expected returns

3.Implied views

Answer 72

• equilibrium’ expected returns for a particular portfolio of assets and covariance matrix

– let the model determine expected returns conditional on the variance-covariance metrics so that a user-specified portfolio (the benchmark) is on the efficient frontier

Question 73

Methods for calibrating expected returns

4.Bayesian techniques, e.g. James Stein

Answer 73

• combine prior information with new information to generate a more refined estimate
• “shrinking” the individual sample means toward a common value referred to as the grand mean

Expect future, some assets are going to be over valued and under valued, over time they will convert. That is the grand mean

Question 74

Lack of reliable data history

Answer 74

•Likely problem areas:

a) New assets
b) Illiquid assets, especially where appraisal-based
c) Structural change
d) Latent, unobserved risks (e.g. liquidity back holes, peso problem)

Large outliers in the data

Question 75

Lack of reliable data history

Lack of reliable data history

•Some responses:

–Adjust the available data series, e.g. ‘de-smooth’ illiquid asset returns, shorten the estimation period, review effect of outliers

Answer 75

“de-smooth” illiquid assets: find out how the smoothing is incorporated in the valuation model and extract the “innovation” and get series of data that is stripped off the smoothing.

Question 76

Lack of reliable data history

Lack of reliable data history

•Some responses:

–Interpolate from like assets given fundamental nature, e.g. is the asset equity or bond-like?; exposure to factors or fundamental risk

example

Answer 76

Example: hedge funds – found volatility is due to equity exposure, examine how much it’s correlated with equity market index, forecast returns that incorporate such equity exposure. Might not be perfect but better than nothing or having something irrelevant.

private equity fund – similar industry/sized investment

Question 77

Lack of reliable data history

•Likely problem areas:

a) New assets
b) Illiquid assets, especially where appraisal-based
c) Structural change
d) Latent, unobserved risks (e.g. liquidity back holes, peso problem)
e) Large outliers in the data (think twice before removing!)

•Some responses:

Answer 77

–Interpolate from like assets given fundamental nature, e.g. is the asset equity or bond-like?; exposure to factors or fundamental risk

–Draw on other representative data, e.g. a close proxy asset

–Adjust the available data series, e.g. ‘de-smooth’ illiquid asset returns, shorten the estimation period, review effect of outliers

–Ad-hoc adjustments (are they better than nothing?)

Question 78

Lack of reliable data history

liquidity black holes

Answer 78

market-makers (investment banks, hedge funds) sell aggressively, market takes a spiral dip, no one is buying, any buy order is absorbed by market immediately.